package com.github.kezhenxu94.playground.leetcode;

import java.util.Arrays;

/**
 * 64. Minimum Path Sum
 * 
 * Given a m x n grid filled with non-negative numbers, find a path from top
 * left to bottom right which minimizes the sum of all numbers along its path.
 * 
 * Note: You can only move either down or right at any point in time.
 * 
 * [Tags] Dynamic Programming
 * 
 * @author ke.zhen.xu
 *
 */
public class Solution064MinimumPathSum {

	public int minPathSum(int[][] grid) {
		if (grid == null || grid.length == 0)
			return 0;
		int[][] dp = new int[grid.length][grid[0].length];
		for (int i = 0; i < grid.length; i++)
			Arrays.fill(dp[i], Integer.MAX_VALUE);
		dp[0][0] = grid[0][0];

		for (int i = 1; i < grid.length; i++)
			dp[i][0] = dp[i - 1][0] + grid[i][0];
		for (int i = 1; i < grid[0].length; i++)
			dp[0][i] = dp[0][i - 1] + grid[0][i];

		for (int i = 1; i < grid.length; i++) {
			for (int j = 1; j < grid[i].length; j++) {
				dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
			}
		}
		return dp[grid.length - 1][grid[0].length - 1];
	}
}
